Grade 5 Long Division: Unit Review

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   2298 ÷ 47 = ?

   1. Start with 229, the first part of 2298 that is at least 47.
   2. 229 ÷ 47: 47 × 4 = 188 (47 × 5 = 235 is too big). Write 4. 229 − 188 = 41. Bring down the 8 to make 418.
   3. 418 ÷ 47: 47 × 8 = 376 (47 × 9 = 423 is too big). Write 8. 418 − 376 = 42.
   4. 2298 ÷ 47 = 48 R42
   5. Check: 48 × 47 + 42 = 2298

   Answer: 48 R42

2. Example 2

   A library is packing 664 books into boxes. Each box holds 15 books. How many boxes are needed to pack all of the books?

   1. We know the total (664) and how many fit in one group (15), and we want how many groups. That is division: 664 ÷ 15.
   2. 664 ÷ 15: take away 15 × 40 = 600 (64 left), 15 × 4 = 60 (4 left). 40 + 4 = 44, so 664 ÷ 15 = 44 R4.
   3. 44 boxes hold 660, but 4 more still need a place, so one more is needed: 44 + 1 = 45.
   4. So the answer is 45 boxes.

   Answer: 45

3. Example 3

   331 students are going on a field trip. Each bus holds 44 students. How many buses are needed so every student has a seat?

   1. We know the total (331) and how many fit in one group (44), and we want how many groups. That is division: 331 ÷ 44.
   2. 331 ÷ 44 = 7 R23: 44 × 7 = 308, and 331 − 308 = 23 left over.
   3. 7 buses hold 308, but 23 more still need a place, so one more is needed: 7 + 1 = 8.
   4. So the answer is 8 buses.

   Answer: 8